Problem Set 7
Political Economy (ECON 452)
1) Suppose we have the following game below:
Row
C
N
Column
C
N
(2,-2)
(-1,1)
(0,0)
(1,-1)
A) If Row knew that Column would pick C with a probability of 100%, what should
Row’s optimal strategy be? What utility would Row expect from this strategy?
B) If Row knew that Column would pick C with a probability of 25%, what should
Row’s optimal strategy be? What utility would Row expect from this strategy?
2) Suppose we model the electoral conflict in 2004 in Ukraine between supporters of
Yushchenko and Yanukovych as a game. Let’s say Yanukovych (who is already in
power, and who won the disputed election) can either call for new elections or simply
claim power. Let’s say Yushchenko can either attempt to gain power through protesting,
or concede defeat.
The utilities of the outcomes are:
1) Yan. calls for new elections, Yush. concedes defeat: (+2 for Yan., -2 for Yush.)
2) Yan. claims power, Yush. concedes defeat: (+6 for Yan., -10 for Yush.)
3) Yan. calls for new elections, Yush. protests: (-2 for Yan., +5 for Yush.)
4) Yan. claims power, Yush. protests: (-4 for Yan., +4 for Yush.)
A) Does either player have a dominant strategy? If so, what is it?
B) Are there any Nash equilibria? If so, what?
3) Consider this model of conflict between Rwanda and Congo. Both countries can either
send troops to their border or negotiate. Rwanda prefers that Congo does not send troops,
and secondarily prefers sending troops. Congo prefers that Rwanda does not send troops;
if Rwanda does send troops, Congo prefers to also send troops, but if Rwanda does not,
Congo prefers to negotiate.
A) Write the matrix of a 2 × 2 ordinal game representing this situation where each
side is assigned ordinal rankings from 4 (best outcome) to 1 (worst outcome).
Determine the Nash equilibrium.
B) Starting from the Nash equilibrium, with Rwanda moving first, use the Theory of
Moves to determine whether the two sides will move away from the Nash
equilibrium.
C) Do the same thing with Congo moving first.